So-called electron loading in radio-frequency (RF) accelerating cavities is the primary cause for cavity performance limitations today. Electron loading can limit the desired energy gain, add cryogenic heat load, damage accelerator components and increase accelerator downtime depending on the induced trip rates. Trip rates are of particular concern for next generation facilities such as Accelerator Driven Subcritical Reactors or Energy Recovery Linacs for Free Electron Lasers.
Electron loading can be attributed to mainly three phenomena, i.e. field emission (FE), multiple impact electron amplification (short: multipacting) and RF electrical breakdown. In all cases, electrons are involved either being released from the enclosing RF surfaces or generated directly within the RF volume by ionization processes with the rest gas (even in ultra-high vacuum), e.g. due to cosmic radiation. The free electrons can absorb a considerable amount of the RF energy provided by external power sources thereby constraining the achievable field level and/or causing operational failures.
Field emission has been a prevalent issue, particularly in superconducting RF (SRF) cavities, whereas RF electrical breakdown and multipacting can be controllable within limits by adequate design choices. Though SRF cavities may readily exceed accelerating fields (Eacc) of 20 MV/m, the onset of parasitic electron activities may start at field levels as low as a few MV/m. Field emission becomes a major concern when the electrons emitted are captured by the accelerating RF field and directed close to the beam axis through a series of cavities or cryomodules.
The free electrons can then accumulate a comparable amount of energy as the main beam would over the same distance. This can present a considerable ‘dark current’ with damaging risks (e.g. when hitting undulator magnets). The electrons can be directed either down- or upstream the accelerator depending on the site and time of origin.
FIG. 1 exemplarily shows the energy range of field-emitted electrons numerically computed for an upgrade cryomodule of Jefferson Lab's electron recirculator CEBAF depending on the initial field emitter location along the cryomodule. The upgrade cryomodule, housing eight seven-cell cavities, covers all probable emitter sites seeded around irises, where the electrical surface field peaks (Epeak). The energies are plotted over the initial 8×8 iris regions covering all possible field emitting surfaces. The 8 sets of data points for each cavity along the x-axis represent same iris regions (1 through 8 for each cavity). A code is given in the legend with C=cavity and I=iris with the corresponding number denoting the site of origin.
The concern with field emission stems from its exponential increase with Eacc (the acceleration gradient), which is well verified experimentally. Note that FE is a quantum-mechanical process that can be described by the (simplified) Fowler-Nordheim (FN) equation:
                    J        =                              I                          A              eff                                =                                                                                          (                                                                  β                        enh                                            ·                                              E                        peak                                                              )                                    2                                ϕ                            ·              a              ·                              10                                  4.52                  ·                                      ϕ                                          -                      0.5                                                                                            ⁢                                          ⅇ                                                      0.956                    ·                    b                    ·                                          ϕ                                              3                        /                        2                                                                                                                        β                      enh                                        ·                                          E                      peak                                                                                  .                                                          (        1        )            
J denotes the peak current density (in A/m2) (current I over effective emission area Aeff), Epeak the local surface electrical field (in V/m), Φ the local material work function (in eV), and a and b, which are the 1st and 2nd FN-constants, respectively (a≈1.541434·106 A·eV·V−2 and b≈6.83089−109 eV−3/2·V/m). Field emission requires surface fields in the order of GV/m. Peak fields in SRF cavities however only reach up to a few ten MV/m. Therefore a local field enhancement factor βenh is introduced, which in SRF cavities requires βenh>50 to produce meaningful emission currents. In fact, such large enhancement factors and higher are often encountered depending on the nature of the field emitter.
Emitted electrons eventually hit surfaces internal or external to cavity cryomodules depending on the site and time of origin, which determines trajectories and energies. Upon impact, electrons not only can create additional heating, but also can induce secondary particle showers and gamma rays via bremsstrahlung. This in turn can cause radio-activation of accelerator components once electrons accumulate energies above the threshold for neutron production, which is in the order of 10 MeV for the metals employed. For instance, very high radiation levels and radio-activation due to FE has been a concern in CEBAF upgrade cryomodules. The primary process for neutron production by electrons is the absorption of bremsstrahlung photons, i.e. via photonuclear reactions. The threshold energy can thus be obtained within a few cavity cells depending on field levels.
Maintaining extremely clean environments throughout cavity fabrication, post-processing and assembly is of major importance to mitigate particulates that may create FE sites. However, the existence of field emitters cannot be excluded even when obeying strict protocols following industrial standards. Based on today's experience a large fraction of SRF cavities remain plagued by FE.